Price and risk evaluation system for financial product or its derivatives, dealing system, recording medium storing a price and risk evaluation program, and recording medium storing a dealing program

Abstract

A system for correctly evaluating a price distribution and a risk distribution for a financial product or its derivatives introduces a probability density function generated with a Boltzmann model at a higher accuracy than the Gaussian distribution for a probability density. The system has an initial value setup unit and an evaluation condition setup unit. Initial values include at least one of price, price change rate, and the price change direction of a financial product. The evaluation conditions include at least time steps and the number of trials. The Boltzmann model analysis unit receives the initial values and the evaluation conditions, and repeats simulations of price fluctuation, based on the Boltzmann model using a Monte Carlo method. A velocity/direction distribution setup unit supplies the probability distributions of the price, price change rate, and the price change direction for the financial product to the Boltzmann model analysis unit. A random number generator for a Monte Carlo method employed in the analysis by the Boltzmann model, and an output unit displays the analysis result. A dealing system applies the financial Boltzmann model to option pricing, and reproduces the characteristics of Leptokurcity and Fat-tail by linear Boltzmann equation in order to define risk-neutral and unique probability measures. Consequently, option prices can be evaluated in a risk-neutral and unique manner, taking into account Leptokurcity and Fat-tail of a price change distribution.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS [0001] This application is a Division of and claims priority under 35 USC § 120 from application Ser. No. 09 / 807,963 filed Jun. 1, 2001, and is a National Stage of PCT Application No. PCT / JP00 / 05755, filed Aug. 25, 2000, and claims the benefit of priority under 35 USC § 119 from Japanese Patent Application Nos. P11-242152, filed Aug. 27, 1999 and P2000-219655, filed Jul. 19, 2000, the entire contents of each are incorporated herein by reference.FIELD OF THE INVENTION [0002] The present invention relates to a system for assessing a price distribution or a risk distribution for a financial product or its derivatives, which can rigorously evaluate a price distribution or a risk distribution, including a probability of occurrence of a big price change, based on a Boltzmann model. This system is also capable of analyzing price fluctuation events for the financial product or its derivatives that could not be reproduced by the conventional technique....

AI Technical Summary

Benefits of technology

[0044] The first object of the present invention is to provide a price and risk evaluation system for evaluating a price distribution or a risk distribution for a financial product or its derivatives with applications of a new calculation method, the details of which will be described below. A risk calculation method is also provided, which is capable of treating the fat-tail problems in the financial engineering field associated with underlying assets and their derivatives, and of substantially eliminating defects or drawbacks having existed in the prior art.

Problems solved by technology

However, the conventional technique for evaluating risks for the financial products or the derivatives is not capable of providing sufficiently reliable results, as is known in this field.

This is because that conventional method evaluates risks of financial products based on the Gaussian distribution, and therefore, the probability of occurrence of a big price change is underestimated.

Although the likelihood of occurrence of a big price change is low, such a big price change has a significant influence to investing risks, as compared with situations under the normal price changes.

Accordingly, any risk evaluation methods or systems for financial products can not be reliable in the practical aspect unless the probability for the big price changes is accurately treated.

Another problem is that the conventional risk evaluation technique requires some corrections to a heterogeneous problem, in which the probability density function changes depending on prices, or to a non-linear problem, in which the probability density function used for the evaluation is a non-linear function.

Furthermore, the conventional risk evaluation technique has very limited capabilities for description, definition, and selection of the variables to produce price fluctuations observed in the markets.

In other words, with the conventional technique, the probability density function can not be sufficiently evaluated with variables for describing risks for financial products, if the actual price change distribution of an financial product is located out of the standard Gaussian-type distribution.

The conventional technique is not capable of describing the probability density function for the price change direction as well, and therefore, the probability distribution of the price change direction for the financial products are disregarded.

Further problems in actual application of the conventional risk evaluation method for financial products relate to insufficient numerical techniques, such as random number sampling and variance reduction areas for making Monte Carlo calculations.

Consequently, undesirable variance inevitably remains in the conventional technique.

However, the conventional dealing systems have many problems listed below in item (1) through (8).

Once if this fact would be introduced from the early state, evolution theoretical financial engineering deployment and implementation to a computer system would have become much more difficult in actual application.

However, these methods have drawbacks in actual application for some reasons.

For example, if transaction is not active enough, there is no continuity in the movement for the price of the underlying assets.

Even in the case that the transaction is active, the conventional methods are not suitable to estimate the volatility under the fat-tailed regime because these methods assume normality in the risk probability distribution for the market behaviors.

However, in a non-active market (for instance, the option transaction market for underlying assets in the current Japanese security market), as the number of observed transactions for options is small, the implied volatility for the corresponding options cannot be well-defined from the actual market data.

On the other hand, in some cases that under the transactions in moderately active market, the option prices observed in the market are scattered in a wide range, it becomes difficult to grasp a comprehensive trend.

However, because these models assume normality in the probability distributions, they can not deal with the Fat-Tail problem sufficiently.

Therefore, this technique is not suitably used in a non-active option market.

However, the jump model has an assumption of discontinuous price fluctuation, and therefore, the stochastic volatility model (SVM) naturally becomes a nonlinear problem.

For this reason, the risk-neutral measure can not be achieved invariably, which prevent the option price from being defined uniquely.

(8) In conclusion, no conventional techniques can provide minute and accurate information in real time for solving the Fat-Tail problem and being applicable to a non-active market, although it has been desired for dealers and traders to receive significant smile curves or a volatility matrix on their displays in real time in response to the actual market that changes every moment.

The conventional technique is incapable of automatically acquiring necessary data required for computation in response to requests from the dealers in an interactive manner, and of automatically selecting the optimum model to analyze the market deeply and flexibly.

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